It is known in the art that the velocity of a sound wave in a material depends on the mechanical properties of the material.
A sound wave that reaches a solid at an angle will typically propagate through and along the solid as a combination of three waves, namely, longitudinal, transverse and surface waves, wherein each wave has a different velocity. In bone velocity determination, the longitudinal wave, which is the fastest, is usually measured. The velocity of the longitudinal wave is:
                              V          L                =                                            E              ⁡                              (                                  1                  -                  σ                                )                                                                    ρ                ⁡                                  (                                      1                    +                    σ                                    )                                            ⁢                              (                                  1                  -                                      2                    ⁢                    σ                                                  )                                                                        (        1        )            where E, σ and ρ are, respectively, the Young's Modulus, the Poisson's ratio of lateral contraction to longitudinal extension and the mass density of the material.
In an article entitled, “Osteoporotic Bone Fragility: Detection by Ultrasound Transmission Velocity,” R. P. Heaney et al., JAMA, Vol. 261, No. 20, May 26, 1989, pp. 2986–2990, the Young's Modulus of bone, E, is given empirically as:E=Kρ2  (2)The velocity of the longitudinal sound wave in the bone is then:VL=√{square root over ((E/ρ))}=√{square root over ((Kρ))}  (3)where K is a constant which incorporates a number of factors, such as spatial orientation of the bone structures, inherent properties of the bone material and fatigue damage. Thus, the velocity of a longitudinal wave is a function of the mass density and can be used as an indicator of the quality of bone.
In order to perform in vivo ultrasonic measurements of the mechanical properties of bone, it is necessary to transmit an ultrasonic wave through the soft tissue surrounding the bone. Unfortunately, the thickness of the soft tissue varies along the length of the bone. Also, the soft tissue velocity is not a constant value for all soft tissues. These variations can affect the accuracy of the ultrasound propagation time measurement through the bone. Typically, the variations in thickness of the soft tissue and its velocity are either ignored or an attempt is made to cancel the effects of the soft tissue.
U.S. Pat. No. 5,143,072, the disclosure of which is incorporated herein by reference, describes a method of overcoming the effects of the unknown thickness of the intervening soft tissue, by ensuring that the measurements will be taken when the portion of the path which passes through soft tissue is of a same length for different measurements. A transmitter and two receivers are placed in a collinear configuration parallel to the bone. When a wave is transmitted from the transmitter towards the bone, the wave passes through intervening soft tissue and then travels along the bone. The two receivers detect ultrasonic waves that exit the bone and travel back through soft tissue to the two receivers. Ignoring the soft tissue, the difference between the path from the transmitter to the first receiver and to the second receiver is a segment of bone whose length is the same as the distance between the two receivers. Generally, the soft tissue cannot be ignored. However, if the two receivers are rather close together, the length of the paths in the soft tissue, between the bone and the receivers, will be approximately the same and should, to a certain level of precision, cancel out. In one embodiment described in the above patent document, the receiver/transmitter configuration is rocked and the measurements are taken only when the (shortest) distances between the bone and the two receivers are the same. These distances may be measured using the receivers as transmitter/receivers that bounce a wave off the bone. When the propagation times are equal, the configuration is assumed to be collinear with the bone.
However, even this method has several shortcomings. First, soft tissue velocity is not a constant, rather, it varies with the type of soft tissue. In addition, the propagation paths between the bone and the receivers are not the same for the reflected wave and for the wave from the transmitter, so the calculated acoustic bone velocity may not be correct. Second, the above-described method requires a relatively long portion of flat bone. Thus, only a small number of bones can be tested, using this method, such as the tibia. In addition, since high frequency ultrasonic waves are very lossy, it is not practical to use them for this method.
PCT publication WO 97/13145, the disclosure of which is incorporated herein by reference, describes an alternative method of bone velocity determination, in which a velocity in a significantly shorter portion of bone may be measured. In this publication, several waves are transmitted to the bone and received by one or more receivers. One of the waves travels through both bone and soft tissue and one or more waves travel only through soft tissue. The waves that travel only through soft tissue are used to calculate the soft tissue velocity. The calculated soft tissue velocity is applied to extract the bone velocity from the travel time of the wave that travels through both bone and soft tissue.